

A075245


xvalue of the solution (x,y,z) to 4/n = 1/x + 1/y + 1/z satisfying 0 < x < y < z and having the largest zvalue. The y and z components are in A075246 and A075247.


14



1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 14, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 20, 19, 19, 20, 20, 20, 20, 21, 21, 21
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OFFSET

3,2


COMMENTS

See A073101 for more details.


LINKS

Table of n, a(n) for n=3..82.


MAPLE

A075245:= proc () local t, n, a, b, t1, largex, largez; for n from 3 to 100 do t := 4/n; largez := 0; largex := 0; for a from floor(1/t)+1 to floor(3/t) do t1 := t1/a; for b from max(a, floor(1/t1)+1) to floor(2/t1) do if `and`(type(1/(t11/b), integer), a < b, b < 1/(t11/b)) then if largez < 1/(t11/b) then largez := 1/(t11/b); largex := a end if end if end do end do; lprint(n, largex) end do end proc; # [program derived from A192787] Patrick J. McNab, Aug 20 2014


MATHEMATICA

For[xLst={}; yLst={}; zLst={}; n=3, n<=100, n++, cnt=0; xr=n/4; If[IntegerQ[xr], x=xr+1, x=Ceiling[xr]]; While[yr=1/(4/n1/x); If[IntegerQ[yr], y=yr+1, y=Ceiling[yr]]; cnt==0&&y>x, While[zr=1/(4/n1/x1/y); cnt==0&&zr>y, If[IntegerQ[zr], z=zr; cnt++; AppendTo[xLst, x]; AppendTo[yLst, y]; AppendTo[zLst, z]]; y++ ]; x++ ]]; xLst


CROSSREFS

Cf. A073101, A075246, A075247, A192787.
Sequence in context: A144075 A128929 A257839 * A328301 A129253 A008652
Adjacent sequences: A075242 A075243 A075244 * A075246 A075247 A075248


KEYWORD

hard,nice,nonn


AUTHOR

T. D. Noe, Sep 10 2002


STATUS

approved



